The Avengers were split, half of them on the run from the UN and USA. The cracks were already there, Baron Zemo was just throwing fuel on the fire. I mean go back to Avengers 1 and the only reason they were ever able to come together was the death of Colsen. As Banner said, "I mean, what are we, a team? No, no, no. We're a chemical mixture that makes chaos. We're a time-bomb. "
That bomb just blew in Civil War. And if you watch the movie, it is 100% a Captain America movie...following his struggles and choices. And of course they were holding back, they still cared for each other, I mean I have had fights with my family and friends and never once went all out full destruct mode.